The purpose of cognitive development is to allow our brains and processes to develop to a level that allows us to make appropriate decisions and to learn the things needed to allow us to be what we are. As mentioned above the study of cognitive development is important in that it allows us to determine patterns of development.
Perhaps you mean what is the purpose of the study of cognitive development? The purposes of this branch of study is to discover and understand the processes by which our thinking, perceiving, understanding and other cognitive functions come to be and to develop. For example, it was mistakenly thought for a time in the mid-1950s that infants' brains were quiet empty organs awaiting stimuli to create a something out of a nothing. Cognitive development studies have debunked that idea and revealed that many cognitive functions are hardwired in our brains from birth and that development follows an uneven pattern but one that is consistent across all cultures and abilities.
I'm not certain about using the term "purpose" in regards to cognitive development. Cognitive development is a natural process that is going to happen in all human beings to varying degrees and under a variety of circumstances. Like breathing, it is simply a natural part of life that will happen for any living being of standard development.
I like literaturenerd' idea that humans need time to fully develop cognitively (although I don't think any of us really ever reach our potentials). The process of learning and growing is such an awesome and fun one...I think it's mostly what life is about...and without that aspect of learning and growing....life would be pretty empty.
Cognitive development is very important in the mental growth of a human. Imagine a child being born with full cognitive processes. The world would be a very different place given the child would not need the slow building of their brains. Humans need time to learn about other aspects of their lives, functions, and learning.
Cognitive development makes us truly human and superior to other species; without the ability to think, man is vulnerable since he has lost many of his physical survival skills. The Old Testament story of David and Goliath is an example of the benefits of cognitive development.
The thing that defines human beings (separating them from the rest of the animals) is their ability to think. Cognitive development is, essentially, the process of learning how to think. Thus, you could argue the purpose of cognitive development is to make us human.
Of course, we evolved the ability to develop cognitively for reasons other than "becoming human." The purpose of cognitive development for the earliest humans is a matter of some dispute. Some think it developed in order that people (with their limited physical tools) would be able to hunt animals effectively. Looked at in this way, cognitive development made people better adapted to their environment.